Ordinal Outcome — Distribution Diagnostics & Hypothesis Testing

Table of Contents

• Scope Boundary
• Workflow
• Decision Tree
• Required Inputs
• Code Structure
• Reporting Standards
• Hypothesis Tests
• Example Dataset
• Method Status
• Minimal Smoke Test
• Cross-Skill Interface

Open-source skill.

Scope Boundary

Use this skill when:

• The outcome has a meaningful order and the first need is a nonparametric baseline plus ordinal distribution reporting.
• The goal is to establish an ordered-response checkpoint before ordinal regression or richer modeling.

Do not use this skill when:

• The classes are unordered or collapse naturally to a binary endpoint.
• The design is paired / repeated, survival, or latent-variable rather than cross-sectional ordinal data.

Workflow

Read each step file in workflow/ before executing that step.

Step	Responsibility	Executor	Document	Input	Output
Collect	Collect Inputs	Main Agent	workflow/step01-collect-inputs.md	User input	Structured input summary
Diagnose	Check Distribution	Main Agent	workflow/step02-check-distribution.md	Prior step output	PART 1 code block
Test	Run Primary Test	Main Agent	workflow/step03-run-primary-test.md	Prior step output	PART 2-3 code blocks

Decision Tree

1. CHECK DISTRIBUTION
   ├── Balanced levels (no cell < 5) → standard nonparametric tests
   └── Sparse levels (any cell < 5) → warn, consider collapsing levels

2. GROUP COMPARISON
   ├── 2 groups → Mann-Whitney U + rank-biserial r
   └── 3+ groups → Kruskal-Wallis + pairwise Dunn's + Cliff's delta

3. TREND TEST (if predictor is ordered)
   └── Jonckheere-Terpstra trend test

Required Inputs

Role	What to collect
Outcome (Y)	Variable name, ordered levels (confirm ordering with user)
Group variable	What defines groups, how many levels
Predictors	For recommendation block (not executed)
Covariates	For recommendation block (not executed)

Code Structure

PART 0: Setup & Data Loading
PART 1: Distribution Diagnostics → plot_01_ordinal_distribution.png
PART 2: Primary Hypothesis Test  → plot_02_stacked_bar_[var].png
PART 3: Recommendation Block     → text listing additional analyses available

Reporting Standards

1. p-values: "< .001" not "0.000"; exact to 3 decimals otherwise
2. Effect sizes: rank-biserial r (Mann-Whitney), Cliff's delta (2 groups), epsilon-squared (Kruskal-Wallis)
3. Always report medians and IQRs for ordinal data, not means/SDs
4. Mann-Whitney U: U = X, p = .XXX, rank-biserial r = .XXX
5. Kruskal-Wallis: H(df) = X.XX, p = .XXX
6. Proportions per level: report as percentages with 1 decimal
7. Non-significance: "not statistically significant at α = .05" — never "no effect"

Hypothesis Tests

Scenario	Test	Effect Size
2 independent groups	Mann-Whitney U	Rank-biserial r
3+ independent groups	Kruskal-Wallis + Dunn's	Cliff's delta (pairwise)
Ordered groups (trend)	Jonckheere-Terpstra	—

Paired/repeated designs → vera-data-repeated-reviewing.

Example Dataset

R: vcd::Arthritis — Outcome = Improvement (None/Some/Marked), Predictors: Treatment, Sex, Age. Python: reconstruct via statsmodels.datasets or manual construction from R dataset.

Method Status

Status	Methods
Implemented in this skill	Ordinal frequency diagnostics, Mann-Whitney / Kruskal-Wallis testing, effect sizes for ordered outcomes, Jonckheere-Terpstra trend testing
Implemented downstream in vera-data-ordinal-generating	Proportional-odds, Brant testing, adjacent-category / continuation-ratio / stereotype models, ordinal-aware trees
Out of scope in this open-source baseline	Unordered multi-class models, repeated ordinal workflows, and ordinal families not named above

Minimal Smoke Test

• Smoke-test prompt: "Run vera-data-ordinal-reviewing on the Arthritis example, treating Improvement as the ordinal outcome and Treatment as the primary grouping variable. Produce the standard baseline artifacts."

Cross-Skill Interface

Output:
├── code_r      → .R script
├── code_python → .py script
├── figures/    → 2 PNGs (ordinal distribution + stacked bar)
└── recommendations → text block (additional analyses available)

Note: proportional-odds logistic regression and Brant/parallel-regression test for PO assumption are delivered by vera-data-ordinal-generating.

Next step: Invoke vera-data-ordinal-generating from this skillset to run the full pipeline (additional tests, subgroup analysis, modeling, manuscript generation). See ../../CROSS-SKILL-INTERFACE.md for the shared handoff contract.